Question
An urn contains 6 red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?
Answer: Option D
P(None is blue),
$$\eqalign{
& = \frac{{^8{C_3}}}{{^{13}{C_3}}} \cr
& = \frac{{56}}{{286}} \cr
& = \frac{{28}}{{143}} \cr} $$
P(At least one is blue),
$$\eqalign{
& = 1 - \frac{{28}}{{143}} \cr
& = \frac{{115}}{{143}} \cr} $$
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P(None is blue),
$$\eqalign{
& = \frac{{^8{C_3}}}{{^{13}{C_3}}} \cr
& = \frac{{56}}{{286}} \cr
& = \frac{{28}}{{143}} \cr} $$
P(At least one is blue),
$$\eqalign{
& = 1 - \frac{{28}}{{143}} \cr
& = \frac{{115}}{{143}} \cr} $$
Was this answer helpful ?
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